Locks
Math/Grade 7
Locks
Briefcase Lock
Many briefcases come with a lock that contains a 3-digit code. Each digit
is chosen from 0-9 and the digits must be put in the correct order for the
lock to open. How many different codes are possible for the briefcase if a
digit may be repeated?
If the lock manufacturer adds an additional digit to the code, how many more combinations are now
available?
Locker Lock
Lockers are often secured with dial locks. The dial contains numbers from 0 to 49.
The combination contains 3 numbers entered in order.
How many different combinations are possible if all the numbers must be different?
How many different combinations are possible if the third number must be different
than the second number but can be a repeat of the first digit?
Safe Lock
Some safe come with dial locks as well that have number from 0-99. How many
different combinations are possible if all the number must be different?
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Locks
Math/Grade 7
Create your own lock:
You are challenged with creating a lock of your own. In designing your lock, consider the following
questions:
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What will your lock be used to protect?
What type of lock will it be?
How will the user have to enter the combination? Is there a dial, keypad, combo, or other way
to enter the code?
How many different combinations are there? What math is used to determine all of the
possibilities?
Why should your lock be considered over other possible locks?
What are some characteristics about your lock that make it unique or different?
Write a short report about your lock. Be sure to include the above information in your report. Also,
include a sketch of your design.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Locks
Math/Grade 7
Locks – Answer Key
Briefcase Lock
Many briefcases come with a lock that contains a 3-digit code. Each digit
is chosen from 0-9 and the digits must be put in the correct order for the
lock to open. How many different codes are possible for the briefcase if a
digit may be repeated?
10 x 10 x 10 = 1000
If the lock manufacturer adds an additional digit to the code, how many more combinations are now
available?
10 x 10 x 10 x 10 = 10,000 There are 9,000 more codes than if there are just 3 digits.
Locker Lock
Lockers are often secured with dial locks. The dial contains numbers from 0 to 49.
The combination contains 3 numbers entered in order.
How many different combinations are possible if all the numbers must be different?
50 x 49 x 48 = 117,600
How many different combinations are possible if the third number must be different
than the second number but can be a repeat of the first digit?
50 x 49 x 49 = 120,050
Safe Lock
Some safe come with dial locks as well that have number from 0-99. How many
different combinations are possible if all the number must be different?
100 x 99 x 98 = 970,200
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project